diff --git a/mesonbuild/environment.py b/mesonbuild/environment.py
index c29657364..3d5d3ab2d 100644
--- a/mesonbuild/environment.py
+++ b/mesonbuild/environment.py
@@ -83,7 +83,7 @@ from .compilers import (
 
 build_filename = 'meson.build'
 
-def detect_gcovr(version='3.1', log=False):
+def detect_gcovr(min_version='3.3', new_rootdir_version='4.2', log=False):
     gcovr_exe = 'gcovr'
     try:
         p, found = Popen_safe([gcovr_exe, '--version'])[0:2]
@@ -91,10 +91,10 @@ def detect_gcovr(version='3.1', log=False):
         # Doesn't exist in PATH or isn't executable
         return None, None
     found = search_version(found)
-    if p.returncode == 0:
+    if p.returncode == 0 and mesonlib.version_compare(found, '>=' + min_version):
         if log:
             mlog.log('Found gcovr-{} at {}'.format(found, shlex.quote(shutil.which(gcovr_exe))))
-        return gcovr_exe, mesonlib.version_compare(found, '>=' + version)
+        return gcovr_exe, mesonlib.version_compare(found, '>=' + new_rootdir_version)
     return None, None
 
 def find_coverage_tools():
diff --git a/mesonbuild/scripts/coverage.py b/mesonbuild/scripts/coverage.py
index 0e203f9b8..4bd41fe91 100644
--- a/mesonbuild/scripts/coverage.py
+++ b/mesonbuild/scripts/coverage.py
@@ -22,35 +22,33 @@ def coverage(outputs, source_root, subproject_root, build_root, log_dir):
 
     (gcovr_exe, gcovr_new_rootdir, lcov_exe, genhtml_exe) = environment.find_coverage_tools()
 
-    # gcovr >= 3.1 interprets rootdir differently
+    # gcovr >= 4.2 requires a different syntax for out of source builds
     if gcovr_new_rootdir:
-        gcovr_rootdir = build_root
+        gcovr_base_cmd = [gcovr_exe, '-r', source_root, build_root]
     else:
-        gcovr_rootdir = source_root
+        gcovr_base_cmd = [gcovr_exe, '-r', build_root]
 
     if not outputs or 'xml' in outputs:
         if gcovr_exe:
-            subprocess.check_call([gcovr_exe,
-                                   '-x',
-                                   '-r', gcovr_rootdir,
+            subprocess.check_call(gcovr_base_cmd +
+                                  ['-x',
                                    '-e', subproject_root,
                                    '-o', os.path.join(log_dir, 'coverage.xml'),
                                    ])
             outfiles.append(('Xml', pathlib.Path(log_dir, 'coverage.xml')))
         elif outputs:
-            print('gcovr needed to generate Xml coverage report')
+            print('gcovr >= 3.3 needed to generate Xml coverage report')
             exitcode = 1
 
     if not outputs or 'text' in outputs:
         if gcovr_exe:
-            subprocess.check_call([gcovr_exe,
-                                   '-r', gcovr_rootdir,
-                                   '-e', subproject_root,
+            subprocess.check_call(gcovr_base_cmd +
+                                  ['-e', subproject_root,
                                    '-o', os.path.join(log_dir, 'coverage.txt'),
                                    ])
             outfiles.append(('Text', pathlib.Path(log_dir, 'coverage.txt')))
         elif outputs:
-            print('gcovr needed to generate text coverage report')
+            print('gcovr >= 3.3 needed to generate text coverage report')
             exitcode = 1
 
     if not outputs or 'html' in outputs:
@@ -101,21 +99,20 @@ def coverage(outputs, source_root, subproject_root, build_root, log_dir):
                                    '--branch-coverage',
                                    covinfo])
             outfiles.append(('Html', pathlib.Path(htmloutdir, 'index.html')))
-        elif gcovr_exe and gcovr_new_rootdir:
+        elif gcovr_exe:
             htmloutdir = os.path.join(log_dir, 'coveragereport')
             if not os.path.isdir(htmloutdir):
                 os.mkdir(htmloutdir)
-            subprocess.check_call([gcovr_exe,
-                                   '--html',
+            subprocess.check_call(gcovr_base_cmd +
+                                  ['--html',
                                    '--html-details',
                                    '--print-summary',
-                                   '-r', build_root,
                                    '-e', subproject_root,
                                    '-o', os.path.join(htmloutdir, 'index.html'),
                                    ])
             outfiles.append(('Html', pathlib.Path(htmloutdir, 'index.html')))
         elif outputs:
-            print('lcov/genhtml or gcovr >= 3.2 needed to generate Html coverage report')
+            print('lcov/genhtml or gcovr >= 3.3 needed to generate Html coverage report')
             exitcode = 1
 
     if not outputs and not outfiles: